Optimal. Leaf size=31 \[ -\frac {a B+A b}{3 x^3}-\frac {a A}{5 x^5}-\frac {b B}{x} \]
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Rubi [A] time = 0.02, antiderivative size = 31, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {448} \[ -\frac {a B+A b}{3 x^3}-\frac {a A}{5 x^5}-\frac {b B}{x} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right ) \left (A+B x^2\right )}{x^6} \, dx &=\int \left (\frac {a A}{x^6}+\frac {A b+a B}{x^4}+\frac {b B}{x^2}\right ) \, dx\\ &=-\frac {a A}{5 x^5}-\frac {A b+a B}{3 x^3}-\frac {b B}{x}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 33, normalized size = 1.06 \[ \frac {-a B-A b}{3 x^3}-\frac {a A}{5 x^5}-\frac {b B}{x} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 29, normalized size = 0.94 \[ -\frac {15 \, B b x^{4} + 5 \, {\left (B a + A b\right )} x^{2} + 3 \, A a}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 31, normalized size = 1.00 \[ -\frac {15 \, B b x^{4} + 5 \, B a x^{2} + 5 \, A b x^{2} + 3 \, A a}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 28, normalized size = 0.90 \[ -\frac {B b}{x}-\frac {A a}{5 x^{5}}-\frac {A b +B a}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.40, size = 29, normalized size = 0.94 \[ -\frac {15 \, B b x^{4} + 5 \, {\left (B a + A b\right )} x^{2} + 3 \, A a}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 29, normalized size = 0.94 \[ -\frac {B\,b\,x^4+\left (\frac {A\,b}{3}+\frac {B\,a}{3}\right )\,x^2+\frac {A\,a}{5}}{x^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.37, size = 32, normalized size = 1.03 \[ \frac {- 3 A a - 15 B b x^{4} + x^{2} \left (- 5 A b - 5 B a\right )}{15 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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